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  1. (1 other version)Cut-rule axiomatization of the syntactic calculus NL.Wojciech Zielonka - 2000 - Journal of Logic, Language and Information 9 (3):339-352.
    An axiomatics of the product-free syntactic calculus L ofLambek has been presented whose only rule is the cut rule. It was alsoproved that there is no finite axiomatics of that kind. The proofs weresubsequently simplified. Analogous results for the nonassociativevariant NL of L were obtained by Kandulski. InLambek's original version of the calculus, sequent antecedents arerequired to be nonempty. By removing this restriction, we obtain theextensions L 0 and NL 0 ofL and NL, respectively. Later, the finiteaxiomatization problem for L (...)
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  • Cut-Rule Axiomatization of the Syntactic Calculus L0.Wojciech Zielonka - 2001 - Journal of Logic, Language and Information 10 (2):233-236.
    In Zielonka (1981a, 1989), I found an axiomatics for the product-free calculus L of Lambek whose only rule is the cut rule. Following Buszkowski (1987), we shall call such an axiomatics linear. It was proved that there is no finite axiomatics of that kind. In Lambek's original version of the calculus (cf. Lambek, 1958), sequent antecedents are non empty. By dropping this restriction, we obtain the variant L0 of L. This modification, introduced in the early 1980s (see, e.g., Buszkowski, 1985; (...)
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